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Neutron Stars 4: Magnetism. Andreas Reisenegger ESO Visiting Scientist Associate Professor, Pontificia Universidad Católica de Chile. Bibliography.

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neutron stars 4 magnetism

Neutron Stars 4: Magnetism

Andreas Reisenegger

ESO Visiting Scientist

Associate Professor,

Pontificia Universidad Católica de Chile

  • Alice Harding & Dong Lai, Physics of strongly magnetized neutron stars, Rep. Prog. Phys., 69, 2631 (2006): includes interesting physics (QED, etc.) that occurs in magnetar-strength fields - not covered in this presentation
  • A. Reisenegger, conference reviews:
    • Origin & evolution of neutron star magnetic fields, astro-ph/0307133: General
    • Magnetic fields in neutron stars: a theoretical perspective, astro-ph/0503047: Theoretical
  • Classes of NSs, evidence for B
  • Comparison to other, related stars, origin of B in NSs
  • Observational evidence for B evolution
  • Physical mechanisms for B evolution
    • External: Accretion
    • Internal: Ambipolar diffusion, Hall drift, resistive decay

Caution: Little is known for sure – many speculations!

spin down magnetic dipole model
Spin-down(magnetic dipole model)

Spin-down time (age?):

Magnetic field:

Lyne 2000,



Kaspi et al. 1999

Classical pulsars

Millisecond pulsars

magnetic field origin
Magnetic field origin?
  • Fossil: flux conservation during core collapse:
    • Woltjer (1964) predicted NSs with B up to ~1015G.
  • Dynamo in convective, rapidly rotating proto-neutron star?
    • Scaling from solar dynamo led to prediction of “magnetars” with B~1016G (Thompson & Duncan 1993).
  • Thermoelectric instability due to heat flow through the crust of the star (Urpin & Yakovlev 1980; Blandford et al. 1983):
    • Field 1012G confined to outer crust (easier to modify)
    • Does not generate magnetar-strength fields
flux freezing
Flux freezing
  • tdecay is long in astrophysical contexts (r large), >> Hubble time in NSs (Baym et al. 1969)  “flux freezing”
  • Alternative: deform the “circuit” in order to move the magnetic field  MHD

Speculation: “Magnetic strip-tease”

  • Upper main sequence stars produce B fields in their convective cores, not their radiative envelopes. Later they lose most of the envelope, leaving a WD or NS.
  • At very high masses, the WD or NS forms only of magnetized material, so it is fully magnetic.
  • At lower masses, the magnetized material is confined to the core of the WD & not visible on the surface.
stable magnetic configurations
Stable magnetic configurations

Pure toroidal & pure poloidal field configurations are unstable, but in combination they can stabilize each other.

(Simulations: Braithwaite & Spruit 2004)

evidence for b field evolution
Evidence for B-field evolution
  • Magnetars:
    • B decay as main energy source?

requires internal field ~10x inferred dipole

  • Young NSs have strongB (classical pulsars, HMXBs), old NSs have weakB (MSPs, LMXBs).

Result of accretion?

  • (Classical) Pulsar population statistics: no decay? - contradictory claims (Narayan & Ostriker 1990; Bhattacharya 1992; Regimbau & de Freitas Pacheco 2001)
  • “Braking index” in young pulsars

 progressive increase of inferred B

x ray binaries
High-mass companion (HMXB):


X-ray pulsars: magnetic chanelling of accretion flow

Cyclotron resonance features  B=(1-4)1012G

Low-mass companion (LMXB):

Likely old (low-mass companions, globular cluster environment)

Mostly non-pulsating (but QPOs, ms pulsations): weak magnetic field

X-ray binaries
origin evolution of pulsars
“Classical” radio pulsars

born in core-collapse supernovae

evolve to longer period

eventually turn off

Millisecond pulsars descend from low-mass X-ray binaries.

Mass transfer in LMXBs produces


(possibly) magnetic field decay

Origin & evolution of pulsars
spin up line
Spin-up line

Alfvén radius: Balance of magnetic vs. gravitational force on accretion flow

  • Equilibrium period: rotation of star matches Keplerian rotation at Alfvén radius


Classical pulsars

Millisecond pulsars

circled: binary systems

Manchester et al. 2002

diamagnetic screening
Diamagnetic screening
  • Material accreted in the LMXB stage is highly ionized  conducting  magnetic flux is frozen
  • Accreted material could screen the original field, which remains inside the star, but is not detectable outside (Bisnovatyi-Kogan & Komberg 1975, Romani 1993, Cumming et al. 2001)


  • Are there instabilities that prevent this?
  • Why is the field reduced to ~ 108-9 G, but not to 0?
another speculation magnetic accretion
Another speculation: Magnetic accretion?

Can the field of MSPs have been transported onto them by the accreted flow?

Force balance:

Mass transport:


  • The strongest magnetic field that can be forced onto a neutron star by an LMXB accretion flow is close to that observed in MSPs.
  • More serious exploration appears warranted:
    • Hydrodynamic model
    • Is the magn. flux transported from the companion star?
    • Is it generated in the disk (“magneto-rotational inst.”)?
    • Is it coherent enough?
chemistry and stratification
“Chemistry” and stratification

(Goldreich & R. 1992)

NS core is a fluid mix of degenerate fermions: neutral (n) and charged (p+, e-)

Chemical equilibrium through weak interactions, e.g., p++ e-  n + e density-dependent mix.

Stable chemical stratification (“Ledoux criterion”), stronger than magnetic buoyancy up to B ~ 1017 G.

To advect magnetic flux, need one of:

Real-time adjustment of chemical equilibrium

“Ambipolar diffusion” of charged particles w. r. to n’s (as in star formation).


Protons & electrons move through a fixed neutron background, colliding with each other and with the background (Goldreich & Reisenegger 1992):


  • Ambipolar diffusion: Driven by magnetic stresses (Lorentz force), protons & electrons move together, carrying the magnetic flux and dissipating magnetic energy.
  • Hall drift: Magnetic flux carried by the electric current; non-dissipative, may cause “Hall turbulence” to smaller scales.
  • Ohmic or resistive diffusion: very small on large scales; important for ending “Hall cascade”. May be important in the crust (uncertain conductivity!).

Time scales depend on B (nonlinear!), lengthscales, microscopic interactions.

Cooper pairing (n superfluidity, p superconductivity) is not included (not well understood, but see Ruderman, astro-ph/0410607).

model conclusions
Model conclusions
  • Spontaneous field decay is unlikely for parameters characteristic of pulsars, unless the field is confined to a thin surface layer.
  • Spontaneous field decay could happen for magnetar parameters (Thompson & Duncan 1996).
  • Simulations underway (Hoyos, Valdivia, & R.)
hall drift
Hall drift

Assume that the only mobile charge carriers are electrons (solid neutron star crust or white dwarf):

“Electron MagnetoHydroDynamics” (EMHD)

  • 1st term: Hall drift:
    • field lines transported by electron flow (   B)
    • purely kinematic, non-dissipative, non-linear
    • turbulent cascade to smaller scales?
      • (Goldreich & Reisenegger 1992)
  • 2nd term: Resistive dissipation

Biskamp et al. 1999: w(x,y)=2Bat 3 different timesin 2-D simulation.

  • Turbulence clearly develops.
  • Properties (power spectrum) not quite the same as predicted by Goldreich & Reisenegger (1992).
  • Models of Hall drift in neutron stars:
  • Geppert, Rheinhardt, et al. 2001-04;
  • Hollerbach & Rüdiger 2002, 2004;
  • others.
exact solutions
Exact solutions

Vainshtein et al. (2000):

  • Plane-parallel geometry
  • Evolution governed by Burgers’ eq.
  • Sharp current sheets dissipate magnetic energy
  • Cumming et al. (2003):
    • Axisymmetric geometry
    • Stable equilibrium solution: rigidly rotating electron fluid; constant, poloidal field
  • R. et al., in preparation:
  • Toroidal equilibrium field, unstable to poloidal perturbations
exact solutions27
Exact solutions

Our recent work

(paper in preparation):

  • Evolution of a toroidal field in axisymmetric geometry
  • Also obtain Burgers’ eq., current sheets
  • Toroidal equilibrium solution is unstable
hall drift many open questions
Hall drift: many open questions
  • Are all realistic B-configurations unstable to Hall drift and evolve by the “Hall cascade”?
  • Can the field get “trapped” in a stable configuration for a resistive time scale, as in ordinary MHD (Braithwaite & Spruit 2004) ?
  • What happens in the fluid interior of the star?
  • How is the evolution if all particles are allowed to move?